Hi Ondrej,

> But your observation gave me an idea that actually I should remove the
> explicit names for morphisms in Mapping.thy completely and then you
> wouldn't even notice there are any abstraction and representation
> functions behind the scene.

I would conclude that if abs and rep are completely opaque and do not
appear in user space (cf. find_theorems!), the duplication lookup == rep
is fine.

Concerning the transfer-or-not question, the mapping type is not really
an issue and I don't really mind loosing mapping_eq_iff etc.  However
there are types where transfer is not the only valid approach to conduct
proofs on, e.g. multisets, as far as I can forsee at the moment.  So it
would be too much rush to drop all those fundamental lemmas there.
Maybe future will bring more insight on this.

Cheers,
        Florian

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